Presumably the convention is the usual one that the PE would be taken as zero if the charges were 'infinitely' separated. In this case, a positive PE would mean that the electric field forces would do a positive amount of work on the particles if the particles were allowed to move apart. Is that enough to help you picture what will happen?

Yes I am referring to electric potential energy of a group of point charges, say 2 negative and 1 positive. This group of charges will have a net negative potential energy. What does this mean? What will happen?

Yes I am referring to electric potential energy of a group of point charges, say 2 negative and 1 positive. This group of charges will have a net negative potential energy.

Will it? The total PE of the system will be
[tex]E_p = \frac{Q{_1}Q{_2}}{4\pi \epsilon_0 r_{1, 2}} + \frac{Q{_2}Q{_3}}{4\pi \epsilon_0 r_{2, 3}} + \frac{Q{_3}Q{_1}}{4\pi \epsilon_0 r_{3, 1}}[/tex]
Here, [itex]r_{1, 2}[/itex] and so on are magnitudes of separating distances.
If two of the charges are negative and one is positive, then two of the terms in the sum will be negative and one will be positive, but I don't think you can deduce that the sum will be negative, as you haven't specified how large the charges are, or their separations.

Potential energy can have an arbitrary offset, so the fact that the energy is positive means nothing at all.

But, for systems of point charges, it is conventional to set the zero of energy to be the situation where the charges are infinitely far apart. In this case, a positive potential energy means that some charges are repelling each other and will fly apart unless somehow held. The system as a whole must be unstable.

Thank you guys for clearing things up. Also, I was assuming the charges were equally far apart from one another like at the vertices of an equilateral triangle and that they all had the same magnitude of charge. In which case the U would be negative